The invention generally relates to the field of semiconductor devices, and more specifically to statistical modeling of leakage-current under influence of process variations.
In semiconductor devices, leakage is a quantum phenomenon where mobile charge carriers (electrons or holes) tunnel through an insulating region. Leakage-currents increase exponentially as the thickness of the insulating region decreases. Tunneling leakage-current can also occur across semiconductor junctions between heavily doped P-type and N-type semiconductors. Other than tunneling via the gate insulator or junctions, carriers can also leak between source and drain terminals of a Metal Oxide Semiconductor (MOS) transistor. The primary source of leakage-current occurs inside transistors, but electrons can also leak between interconnects. Leakage-current increases power consumption and if sufficiently large can cause complete circuit failure.
In modern semiconductor technologies leakage-currents are quantities that may vary significantly from die to die due to increasing influence of uncontrollable random process variations. Also, the prediction of reliable margins for the leakage currents that might be expected is a crucial task for all applications with mandatory low power-consumption, e.g. mobile phones.
The usual worst/best-case corner estimates, which are traditionally used to assess the variation range of the leakage currents to be expected for a given design, are of little or no use, because they span a very pessimistic and completely unrealistic prediction range. Log-normal (LN) distributions have been used to predict the leakage-current variations, although the data used to determine the necessary parameters are not based on realistic design data and do not cover the full range of applied voltages and temperatures. Also, it is not uncommon to have a difference of more than one order of magnitude between worst- and best-case corner estimate values, which is far from the realistic distribution width determined e.g. by extensive simulations or by detailed leakage measurements.
Such worst/best-case corner estimate values are of little practical use when the “true” variation behavior is needed and it is, for example, of limited help for the designer of a low power mobile device to know that the achievable battery powered standby time is between one and ten days. Therefore, in order to decide whether a design idea is acceptable or not, the designer needs much more accurate and reliable information on the “true” variation range.